For MFS (Married Filing Separately) with NRA (Nonresident Alien) spouse in past IRS required "NRA" to be typed where the spouse's SSN goes and to paper file. Now in 2023 IRS Publication 501, page 7, the IRS is clear that "NRA" goes where the spouse's name goes and e-filing is allowed. Why isn't the TurboTax software updated to allow e-filing without the SSN. Will this be fixed soon? E-filing is always better than paper filing.
When you say TurboTax won't allow you to do so, where are you being stopped? When it gives you the error or further? If you are stopping at the error, try to go through the error. Here are the current instructions for filing with a NRA spouse separately.
You can try typing NRA in as your spouses last name. Make sure you put a check mark in the box that says My spouse is a Non-Resident alien in the My info section. When you get to the end and try to transmit the return, ignore the e-file errors regarding your NRA spouse and select transmit your return